Question

What is the integral of e^(-4x)dx from 0 to 1?

Answer 1

The integral of e^(-4x)dx from 0 to 1 is determined by first taking the integral of the e^(-4x)dx. The integral of e^(-4x)dx is -1/4 e^-4x. We substitute 0 to this function: This is equal to -1/4. When substituting with 1, the answer is -1/4 e^-4. The answer is 0.25e^4 -1.

Answer 2

`\texttt{We use the formula: } \\ \int ae^(bx) = abe^(bx) ~~~ a,b \in R\\ \\ a=1 \texttt{ and } b=-4\\ \\ \Longrightarrow ~~ \int\limits^0_1 {e^(-4x)} \, dx = -4e^(-4x)\Big|_0^1 = -4e^(-4\cdot 1) - (-4e^(-4\cdot 0) )= \\ \\ = -4e^(-4) +4e^0 = -4e^(-4) +4e^0 = \boxed{-4e^(-4) +4}`